The fractal dimension of drifter trajectories and estimates of horizontal eddy-diffusivity
The fractal dimension of drifter trajectories and estimates of horizontal eddy-diffusivity
复制标题
漂流者轨迹的分形维数和水平涡扩散率的估计
DOI：
10.3402/tellusa.v43i5.11956
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发表时间：
1991
期刊：
影响因子：
2
通讯作者：
D. Booth
中科院分区：
文献类型：
--
作者：
B. Sanderson;D. Booth
本文分析了东北大西洋的漂流物资料，发现在5 ~ 100 km尺度上，单粒子运动的分维D = 1.28 ± 0.08。单粒子的轨迹模型采用分数布朗运动。因此，积分时间尺度被证明是一个函数的位置固定之间的时间和总周期的长度的漂移被跟踪。方差（粒子分散度）大约以t 3/2的形式增长。单粒子速度的概率密度函数被观察到是尖峰，符合分数布朗运动模型。目前的工作报告的两个粒子的轨迹与分形维数D = 1.3的尺度从8公里到150公里。两粒子的分散被建模为加速分数布朗运动，其中速度成为时间的函数，因为粒子彼此非常接近。选择的加速度与斑块方差增长t2.34一致。由距离l分开的漂移体对之间的相对速度的依赖性，被观察到缩放为l 0.3。这与两粒子运动的加速分数布朗运动模型是一致的。DOI：10.1034/j.1600-0870.1991.t01-1-00008.x
We analyse drifter data from the Northeast Atlantic and find that single-particle motion has fractal dimension D = 1.28 ± 0.08 at scales 5 to 100 km. The single particle trajectories are modeled using fractional Brownian motion. Integral time scale is therefore shown to be a function of both the time between position fixes and the length of the total period the drifter was tracked. The variance (particle dispersion) grows as approximately t 3/2 . The probability density function of single-particle velocity is observed to be leptokurtic, consistent with the fractional Brownian motion model. The present work reports two-particle trajectories with fractal dimension D = 1.3 for scales from 8 km to 150 km. The two-particle dispersion is modelled as accelerated fractional Brownian motion, in which speed becomes a function of time elapsed since the particles were very near to each other. The acceleration is chosen to be consistent with the patch variance growing as t 2.34 . The dependence of relative velocity between pairs of drifters separated by a distance l , is observed to scale as l 0.3 . This is consistent with the accelerated fractional Brownian motion model for two-particle motion. DOI: 10.1034/j.1600-0870.1991.t01-1-00008.x